Planarity and multiple components promote organic photovoltaic efficiency by improving electronic transport

Harnessing DFT and machine learning for accurate optical gap prediction in conjugated polymers

Conjugated polymers (CPs), characterized by alternating σ and π bonds, have attracted significant attention for their diverse structures and adjustable electronic properties. However, predicting the optical band gap (Eexpgap) of CPs remains challenging. This study presents a rational model that integrates density functional theory (DFT) calculation with a data-driven machine learning (ML) approach to predict the experimentally measured Eexpgap of CPs, using 1096 data points. Through alkyl side chain truncation and conjugated backbone extension, the modified oligomers effectively capture the electronic properties of CPs, significantly improving the correlation between the DFT-calculated HOMO-LUMO gap (Eoligomergap) and Eexpgap (R2 = 0.51) compared to the unmodified side-chain-containing monomers (R2 = 0.15). Moreover, we trained six ML models with two categories of features as input: Eoligomergap to represent the extended backbone and molecular features of unmodified monomers to capture the alkyl-side-chain effect. The best model, XGBoost-2, achieved an R2 of 0.77 and an MAE of 0.065 eV for predicting Eexpgap, falling within the experimental error margin of ∼0.1 eV. We further validated XGBoost-2 on a dataset of 227 newly synthesized CPs collected from literature without further retraining. Notably, XGBoost-2 exhibits both excellent interpolation for BT-, BTA-, QA-, DPP-, and TPD-based CPs, and exceptional extrapolation for PDI-, NDI-, DTBT-, BBX-, and Y6-based CPs, which are attributed to the integration of DFT methods with rationally designed oligomer structures. For the first time, we demonstrated a novel and effective strategy combining quantum chemistry calculations with ML modeling for accurate and efficient prediction of experimentally measured fundamental properties of CPs. Our study paves the way for the accelerated design and development of high-performance CPs in photoelectronic applications.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Beyond Conformational Control: Effects of Noncovalent Interactions on Molecular Electronic Properties of Conjugated Polymers

Tuning the electronic properties of polymers is of great importance in designing highly efficient organic solar cells. Noncovalent intramolecular interactions have been often used for conformational control to enhance the planarity of polymers or molecules, which may reduce band gaps and promote charge transfer. However, it is not known if noncovalent interactions may alter the electronic properties of conjugated polymers through some mechanism other than the conformational control. Here, we studied the effects of various noncovalent interactions, including sulfur-nitrogen, sulfur-oxygen, sulfur-fluorine, oxygen-nitrogen, oxygen-fluorine, and nitrogen-fluorine, on the electronic properties of polymers with planar geometry using unconstrained and constrained density functional theory. We found that the sulfur-nitrogen intramolecular interaction may reduce the band gaps of polymers and enhance the charge transfer more obviously than other noncovalent interactions. Our findings are also consistent with the experimental data. For the first time, our study shows that the sulfur-nitrogen noncovalent interaction may further affect the electronic structure of coplanar conjugated polymers, which cannot be only explained by the enhancement of molecular planarity. Our work suggests a new mechanism to manipulate the electronic properties of polymers to design high-performance small-molecule-polymer and all-polymer solar cells.

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn-Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

Unexpectedly Large Couplings Between Orthogonal Units in Anthraquinone Polymers

The unusual electronic properties of directly linked 1,4-polyanthraquinones (14PAQs) are investigated. The dihedral angle between the molecular planes of anthraquinones (AQs) is found to be close to 90°. Contrary to the prevailing notion that the interaction between orthogonal units is negligible due to broken π-electron conjugation, the coupling between neighboring AQ units does not have a minimum at 90° and is much larger than that expected. The unexpectedly large electronic coupling between orthogonal AQ units is explained by the interaction between the lone pairs of the carbonyl oxygen and the π system of the neighboring unit, which allows favorable overlap between frontier molecular orbitals at the orthogonal geometry. It is shown that this effect, which is described computationally for the first time, can be strengthened by adding more quinone units. The effect of thermal fluctuations on the couplings is assessed through ab initio molecular dynamics simulations. The distributions of the couplings reveal that electron transport is resilient to dynamic disorder in all systems considered, whereas the hole couplings are much more sensitive to disorder. Lone pair-π interactions are described, as a previously largely overlooked conjugation mechanism, for incorporation into a new class of disorder-resilient semiconducting redox polymers.

Glassy phases in organic semiconductors

Organic semiconductors may be processed from fluids using graphical arts printing and patterning techniques to create complex circuitry. Because organic semiconductors are weak van der Waals solids, the creation of glassy phases during processing is quite common. Because structural disorder leads to electronic disorder, it is necessary to understand these phases to optimize and control the electronic properties of these materials. Here we review the significance of glassy phases in organic semiconductors. We examine challenges in the measurement of the glass transition temperature and the accurate classification of phases in these relatively rigid materials. Device implications of glassy phases are discussed. Processing schemes that are grounded in the principles of glass physics and sound glass transition temperature measurement will more quickly achieve desired structure and electronic characteristics, accelerating the exciting progress of organic semiconductor technology development.

Intra-molecular Charge Transfer and Electron Delocalization in Non-fullerene Organic Solar Cells

Two types of electron acceptors were synthesized by coupling two kinds of electron-rich cores with four equivalent perylene diimides (PDIs) at the α-position. With fully aromatic cores, TPB and TPSe have π-orbitals spread continuously over the whole aromatic conjugated backbone, unlike TPC and TPSi, which contain isolated PDI units due to the use of a tetrahedron carbon or silicon linker. Density functional theory calculations of the projected density of states showed that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for TPB are localized in separate regions of space. Further, the LUMO of TPB shows a greater contribution from the orbitals belonging to the connective core of the molecules than that of TPC. Overall, the properties of the HOMO and LUMO point at increased intra-molecular delocalization of negative charge carriers for TPB and TPSe than for TPC and TPSi and hence at a more facile intra-molecular charge transfer for the former. The film absorption and emission spectra showed evidences for the inter-molecular electron delocalization in TPB and TPSe, which is consistent with the network structure revealed by X-ray diffraction studies on single crystals of TPB. These features benefit the formation of charge transfer states and/or facilitate charge transport. Thus, higher electron mobility and higher charge dissociation probabilities under J_sc condition were observed in blend films of TPB:PTB7-Th and TPSe:PTB7-Th than those in TPC:PTB7-Th and TPSi:PTB7-Th blend films. As a result, the J_sc and fill factor values of 15.02 mA/cm², 0.58 and 14.36 mA/cm², 0.55 for TPB- and TPSe-based solar cell are observed, whereas those for TPC and TPSi are 11.55 mA/cm², 0.47 and 10.35 mA/cm², 0.42, respectively.

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³∑_g ^- and ³∏_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential π-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.

Metal-Insulator Transition in Nanoparticle Solids: Insights from Kinetic Monte Carlo Simulations

Progress has been rapid in increasing the efficiency of energy conversion in nanoparticles. However, extraction of the photo-generated charge carriers remains challenging. Encouragingly, the charge mobility has been improved recently by driving nanoparticle (NP) films across the metal-insulator transition (MIT). To simulate MIT in NP films, we developed a hierarchical Kinetic Monte Carlo transport model. Electrons transfer between neighboring NPs via activated hopping when the NP energies differ by more than an overlap energy, but transfer by a non-activated quantum delocalization, if the NP energies are closer than the overlap energy. As the overlap energy increases, emerging percolating clusters support a metallic transport across the entire film. We simulated the evolution of the temperature-dependent electron mobility. We analyzed our data in terms of two candidate models of the MIT: (a) as a Quantum Critical Transition, signaled by an effective gap going to zero; and (b) as a Quantum Percolation Transition, where a sample-spanning metallic percolation path is formed as the fraction of the hopping bonds in the transport paths is going to zero. We found that the Quantum Percolation Transition theory provides a better description of the MIT. We also observed an anomalously low gap region next to the MIT. We discuss the relevance of our results in the light of recent experimental measurements.

Design of Heterogeneous Chalcogenide Nanostructures with Pressure-Tunable Gaps and without Electronic Trap States

Heterogeneous nanostructures, such as quantum dots (QDs) embedded in solid matrices or core-shell nanoparticles, are promising platforms for a wide variety of applications, including phosphors with increased quantum yield, photocatalysis, and solar energy conversion. However, characterizing and controlling their interfacial morphology and defects, which greatly influence their electronic properties, have proven difficult in numerous cases. Here we carried out atomistic calculations on chalcogenide nanostructured materials, i.e., PbSe QDs in CdSe matrices and CdSe embedded in PbSe, and we established how interfacial and core structures affect their electronic properties. In particular, we showed that defects present at interfaces of PbSe nanoparticles and CdSe matrices give rise to detrimental intragap states, degrading the performance of photovoltaic devices. Instead, the electronic gaps of the inverted system (CdSe dots in PbSe) are clean, indicating that this material has superior electronic properties for solar applications. In addition, our calculations predicted that the core structure of CdSe and in turn its band gap may be tuned by applying pressure to the PbSe matrix, providing a means to engineering the properties of new functional materials.